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Analysis of the newsboy problem with fuzzy demands and incremental discounts

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  • Chen, Shih-Pin
  • Ho, Yann-Horng
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    Abstract

    This paper proposes an analysis method for the single-period (newsboy) inventory problem with fuzzy demands and incremental quantity discounts. In fuzzy environments, the availability of the quantity discount makes the analysis of the associated model more complex. The proposed analysis method is based on ranking fuzzy number and optimization theory. By applying the Yager ranking method, the fuzzy total cost functions with different unit purchasing costs are transformed into convex piecewise nonlinear functions. To effectively and efficiently find the optimal inventory policy, the proofs of two properties regarding the relative position between the price break and minimums of these nonlinear functions are proposed. The closed-form solutions to the optimal order quantities are also derived. Four cases of a numerical example are solved to demonstrate the validity of the proposed analysis method. It is clear that the proposed methodology is applicable to further cases with different types of quantity discounts and other more complicated cases. More importantly, managerial implications are also provided for decision-makers' references.

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    Bibliographic Info

    Article provided by Elsevier in its journal International Journal of Production Economics.

    Volume (Year): 129 (2011)
    Issue (Month): 1 (January)
    Pages: 169-177

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    Handle: RePEc:eee:proeco:v:129:y:2011:i:1:p:169-177

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    Web page: http://www.elsevier.com/locate/ijpe

    Related research

    Keywords: Fuzzy sets Inventory Incremental discounts Newsboy problem Single-period problem;

    References

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    1. Mula, J. & Poler, R. & Garcia-Sabater, J.P. & Lario, F.C., 2006. "Models for production planning under uncertainty: A review," International Journal of Production Economics, Elsevier, vol. 103(1), pages 271-285, September.
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    3. Ishii, Hiroaki & Konno, Tutomu, 1998. "A stochastic inventory problem with fuzzy shortage cost," European Journal of Operational Research, Elsevier, vol. 106(1), pages 90-94, April.
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    5. Serel, Dogan A., 2008. "Inventory and pricing decisions in a single-period problem involving risky supply," International Journal of Production Economics, Elsevier, vol. 116(1), pages 115-128, November.
    6. Monica Lam, S. & Wong, Danny S., 1996. "A fuzzy mathematical model for the joint economic lot size problem with multiple price breaks," European Journal of Operational Research, Elsevier, vol. 95(3), pages 611-622, December.
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    8. Özler, Aysun & Tan, BarIs & Karaesmen, Fikri, 2009. "Multi-product newsvendor problem with value-at-risk considerations," International Journal of Production Economics, Elsevier, vol. 117(2), pages 244-255, February.
    9. Giannoccaro, Ilaria & Pontrandolfo, Pierpaolo & Scozzi, Barbara, 2003. "A fuzzy echelon approach for inventory management in supply chains," European Journal of Operational Research, Elsevier, vol. 149(1), pages 185-196, August.
    10. Petrovic, Dobrila & Petrovic, Radivoj & Vujosevic, Mirko, 1996. "Fuzzy models for the newsboy problem," International Journal of Production Economics, Elsevier, vol. 45(1-3), pages 435-441, August.
    11. Arshinder & Kanda, Arun & Deshmukh, S.G., 2008. "Supply chain coordination: Perspectives, empirical studies and research directions," International Journal of Production Economics, Elsevier, vol. 115(2), pages 316-335, October.
    12. Roy, T.K. & Maiti, M., 1997. "A fuzzy EOQ model with demand-dependent unit cost under limited storage capacity," European Journal of Operational Research, Elsevier, vol. 99(2), pages 425-432, June.
    13. Shi, Jianmai & Zhang, Guoqing, 2010. "Multi-product budget-constrained acquisition and pricing with uncertain demand and supplier quantity discounts," International Journal of Production Economics, Elsevier, vol. 128(1), pages 322-331, November.
    14. Mostard, Julien & de Koster, Rene & Teunter, Ruud, 2005. "The distribution-free newsboy problem with resalable returns," International Journal of Production Economics, Elsevier, vol. 97(3), pages 329-342, September.
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    Cited by:
    1. Su, Rung Hung & Pearn, Wen Lea, 2011. "Product selection for newsboy-type products with normal demands and unequal costs," International Journal of Production Economics, Elsevier, vol. 132(2), pages 214-222, August.
    2. He, Zhou & Wang, Shouyang & Cheng, T.C.E., 2013. "Competition and evolution in multi-product supply chains: An agent-based retailer model," International Journal of Production Economics, Elsevier, vol. 146(1), pages 325-336.

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